New Correspondences of Integrability Structures and Solution Structures with Miura Transformation

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2026-08-01 Epub Date: 2026-09-15 DOI:10.1016/S0034-4877(26)00053-4

Qiulan Zhao, Jie Sun, Runliang Lin, Xinyue Li

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引用次数: 0

Abstract

In this paper, the corresponding relationships of the integrability structures and the solution structures between a dispersionless Kadomtsev-Petviashvili (dKP) equation and a dispersionless modified Kadomtsev-Petviashvili (dmKP) equation are obtained. On the one hand, the equivalence of the conservation laws, potential systems, nonlocal conservation laws and extended potential systems for the two equations are explored. On the other hand, starting from the original equations and the extended potential systems, respectively, we establish the correspondences of the solution structures for these two equations. Furthermore, the discrete symmetries of the dmKP equation are presented. It is worth noting that we link the extended potential system with the Type-II hidden symmetry. This combination provides a new perspective for solving the extended potential system. In addition, this method of further studying equations through the Miura transformation can be applied to other equations as well, and it can help us better analyze these equations.

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基于Miura变换的可积结构与解结构的新对应关系

得到了无色散Kadomtsev-Petviashvili （dKP）方程与无色散修正Kadomtsev-Petviashvili （dmKP）方程的可积结构与解结构的对应关系。一方面，研究了两个方程的守恒律、势系统、非定域守恒律和扩展势系统的等价性。另一方面，分别从原方程和扩展势系统出发，建立了这两个方程解结构的对应关系。进一步，给出了dmKP方程的离散对称性。值得注意的是，我们将扩展势系统与ii型隐藏对称联系起来。这种组合为求解扩展电位系统提供了一个新的视角。此外，这种通过Miura变换进一步研究方程的方法也可以应用于其他方程，可以帮助我们更好地分析这些方程。得到了无色散Kadomtsev-Petviashvili （dKP）方程与无色散修正Kadomtsev-Petviashvili （dmKP）方程的可积结构与解结构的对应关系。一方面，研究了两个方程的守恒律、势系统、非定域守恒律和扩展势系统的等价性。另一方面，分别从原方程和扩展势系统出发，建立了这两个方程解结构的对应关系。进一步，给出了dmKP方程的离散对称性。值得注意的是，我们将扩展势系统与ii型隐藏对称联系起来。这种组合为求解扩展电位系统提供了一个新的视角。此外，这种通过Miura变换进一步研究方程的方法也可以应用于其他方程，可以帮助我们更好地分析这些方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.